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 To cheer you up in difficult times 5: A New Elementary Proof of the Prime Number Theorem by Florian K. Richter
 To cheer you up in difficult times 4: Women In Theory present — I will survive
 To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new hypercontractivity inequality of Peter Keevash, Noam Lifshitz, Eoin Long and Dor Minzer
 Harsanyi’s Sweater
 To cheer you up in difficult times II: Mysterious matching news by Gal Beniamini, Naom Nisan, Vijay Vazirani and Thorben Tröbst!
 Trees not Cubes! Memories of Boris Tsirelson
 A small update from Israel and memories from Singapore: Partha Dasgupta, Robin Mason, Frank Ramsey, and 007
 Game Theory – online Course at IDC, Herzliya
 TYI44: “What Then, To Raise an Old Question, is Mathematics?”
Top Posts & Pages
 To cheer you up in difficult times 5: A New Elementary Proof of the Prime Number Theorem by Florian K. Richter
 Aubrey de Grey: The chromatic number of the plane is at least 5
 To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new hypercontractivity inequality of Peter Keevash, Noam Lifshitz, Eoin Long and Dor Minzer
 Amazing: Hao Huang Proved the Sensitivity Conjecture!
 The seventeen camels riddle, and Noga Alon's camel proof and algorithms
 'Gina Says'
 Jean
 Or Ordentlich, Oded Regev and Barak Weiss: New bounds for Covering Density!
 A Mysterious Duality Relation for 4dimensional Polytopes.
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Search Results for: Hirsch conjecture
Francisco Santos Disproves the Hirsch Conjecture
A title and an abstract for the conference “100 Years in Seattle: the mathematics of Klee and Grünbaum” drew a special attention: Title: “A counterexample to the Hirsch conjecture” Author: Francisco Santos, Universidad de Cantabria Abstract: I have been in … Continue reading
Posted in Convex polytopes, Open problems, Polymath3
36 Comments
The Polynomial Hirsch Conjecture: Discussion Thread, Continued
Here is a link for the justposted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle, Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper by Sandeep Koranne and Anand Kulkarni “The dstep Conjecture is Almost true” – … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Convex polytopes, Hirsch conjecture
16 Comments
The Polynomial Hirsch Conjecture: Discussion Thread
This post is devoted to the polymathproposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Hirsch conjecture, Polytopes
115 Comments
The Polynomial Hirsch Conjecture – How to Improve the Upper Bounds.
I can see three main avenues toward making progress on the Polynomial Hirsch conjecture. One direction is trying to improve the upper bounds, for example, by looking at the current proof and trying to see if it is wasteful and if so where … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Discussion, Hirsch conjecture
14 Comments
The Polynomial Hirsch Conjecture, a Proposal for Polymath3 (Cont.)
The Abstract Polynomial Hirsch Conjecture A convex polytope is the convex hull of a finite set of points in a real vector space. A polytope can be described as the intersection of a finite number of closed halfspaces. Polytopes have … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Hirsch conjecture, Polymath proposals
5 Comments
The Polynomial Hirsch Conjecture: A proposal for Polymath3
This post is continued here. Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a dpolytope with n vertices facets has diameter at most nd. We devoted several … Continue reading
Amazing: Karim Adiprasito proved the gconjecture for spheres!
Karim in his youth with a fan Congratulations, Karim! Update: Here is the link to the paper From the arXive, Dec 26, 2018. (Link will be added tomorrow.) COMBINATORIAL LEFSCHETZ THEOREMS BEYOND POSITIVITY by Karim Adiprasito Abstract: Consider a simplicial complex … Continue reading
Karim Adiprasito: Flag simplicial complexes and the nonrevisiting path conjecture (A combinatorial proof of the AdiprasitoBenedetti theorem.)
This post is authored by Karim Adiprasito The past months have seen some exciting progress on diameter bounds for polytopes and polytopal complexes, both in the negative and in the positive direction. Jesus de Loera and Steve Klee described simplicial polytopes which are not … Continue reading
Posted in Convex polytopes, Guest blogger
Tagged Convex polytopes, Flag complexes, Hirsch conjecture, Karim Adiprasito
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Updates and plans III.
Update on the great Noga’s Formulas competition. (Link to the original post, many cash prizes are still for grab!) This is the third “Updates and plans post”. The first one was from 2008 and the second one from 2011. Updates: Combinatorics and … Continue reading
Posted in Combinatorics, Conferences, Updates
13 Comments
Combinatorics and More – Greatest Hits
Combinatorics and More’s Greatest Hits First Month Combinatorics, Mathematics, Academics, Polemics, … Helly’s Theorem, “Hypertrees”, and Strange Enumeration I (There were 3 follow up posts:) Extremal Combinatorics I: Extremal Problems on Set Systems (There were 4 follow up posts II ; III; IV; VI) Drachmas Rationality, Economics and … Continue reading
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